Quantum Parrondo Games in Low-Dimensional Hilbert Spaces

TL;DR

This paper explores quantum versions of Parrondo games using quantum walks on small cycles, revealing complex win/loss patterns influenced by entanglement and interference in low-dimensional Hilbert spaces.

Contribution

It introduces a novel quantum Parrondo game model based on quantum walks in low-dimensional Hilbert spaces and analyzes its long-term behavior.

Findings

Systematic win or loss observed in long-term limit

Entanglement and interference create complex outcome structures

Quantum walk-based Parrondo game exhibits rich dynamics

Abstract

We consider quantum variants of Parrondo games on low-dimensional Hilbert spaces. The two games which form the Parrondo game are implemented as quantum walks on a small cycle of length $M$. The dimension of the Hilbert space is $2M$. We investigate a random sequence of these two games which is realized by a quantum coin, so that the total Hilbert space dimension is $4M$. We show that in the quantum Parrondo game constructed in this way a systematic win or loss occurs in the long time limit. Due to entaglement and self-interference on the cycle, the game yields a rather complex structure for the win or loss depending on the parameters.